# Gravitational Time Dilation Calculator

Gravitational Time Dilation is the best online tool to find how much slower the time passes near enormous objects by entering the values like mass(m), radius(r), and time interval. To use this calculator, give the above inputs and click on the calculate button so that you will get easy results in a moment of time.

### What do We Mean by Gravitational Time Dilation?

If the change in the lapse of time is caused by the gravitational field, then that is called gravitational time dilation. It is described per the general theory of Einstein. Einstein's theory says that the closer the observer is to a source of gravity and the greater its mass, the slower that time passes.

The formula of Gravitational Time Dilation is,

**Δt' = Δt x √(1 - 2 x M x G / r x c²)**

where,

Δt' = Time interval that is affected by gravity.

M = Mass

r = Distance.

Δt = Time interval that is not affected by gravity.

G = Gravitational Constant = 6.6743 * 10^{-11} N*m^{2}/kg^{2}_{.}

c = Speed of light.

### How to Calculate Gravitational Time Dilation?

Gravitational time dilation can be calculated easily by the calculator tool, but if you follow the steps that we have given, you can easily calculate the gravitational time dilation manually by hand too. Check out the guidelines carefully.

- Note down the values that are given in the problem.
- Next, read the question carefully to know what you need to find.
- And then if you need to find other than gravitational time dilation, rewrite the formula accordingly.
- Or, if you want to find gravitational time dilation itself then apply the formula.
- Substitute the values and simplify them.
- Finally, you will get the answer for gravitational time dilation.

### Gravitational Time Dilation Example

**Example:**

**Question: **A spaceship is reaching the black hole in messier 88. To experience time twice as slowly how close to this black hole must the spaceship get to experience? This black hole weighs around 6.7 billion times as much as our sun, which weighs 1.989 x 10^{30} kg.

**Answer:**

Given values are,

Weight of the black hole,

M = 1.989 x 10^{30} x 6,600,000,000 = 1.3127 x 10^{40} kg.c = 299,792,458 m/s

G = 6.7 x 10^{-11} N*(m/kg)^{2}

Δt = 1

Δt' = 0.5

r =?

Rewrite the formula equation

r = -2GM/c^{2}((Δt'/Δt)^{2-1})

r = -2(6.7x10^{-11})(1.3127x10^{40}) / (-.75)(299,792,458)^{2}

r = -2(56)(1365.208) / (-0.75)(299,792,458)^{2}.

r = 1,52,903.296 / 6.740663840526132 x 10^{16}

r = 4.40 x 10^{16} m.

Therefore, the value of the radius is 4.40 x 10^{16} m.

For more exciting calculators like this, you can check on to physicscalculatorpro.com website.

### FAQs on Gravitational Time Dilation Calculator

**1. What is gravitational time dilation?**

Gravitational time dilation is nothing but the change in the time-lapse caused by a gravitational force.

**2. How do you use this gravitational time dilation calculator?**

To use this gravitational time dilation calculator, simply provide the inputs in the input fields and click on the calculate button that gives you instant results.

**3. What is the best tool to calculate gravitational time dilation?**

The gravitational time dilation calculator tool is the best online tool to calculate gravitational time dilation.

**4. What is the formula of gravitational time dilation?**

The formula of gravitational time dilation is **r = -2GM/c ^{2}((Δt'/Δt)^{2-1}).**